Warmer air continues to make a run at the Dakotas but is hindered by the large and deep mass of arctic air plopped across the Upper Plains. As the warm air pushes up and over that frigid mass, it will produce widespread cloud cover and some light snow. A warm front will result in rising temperatures Saturday night. That could result in a a dusting to maybe half an inch of snow. That will be followed by a warmer Sunday for most of the area.
Temperatures should push close to 30° by Sunday afternoon for points south of Rapid City. However, the colder air will linger to the north. Temperatures will likely stay in the single digits up that way.
Monday brings another cold front and the progress built over the weekend will be lost. Arctic air crashes back into the area for the remainder of the week. Next week looks just as cold as this week. Medium range weather models point to a good chance of snow by next weekend.